Free Rotation of a Rigid Mass Carrying a Rotor with an Internal Torque

Abstract

Abstract Purpose In this paper, the analytic solution for a free rotatory motion under the influence of a motor of limited power is investigated; we aim to prove that the motion of the carrier body is close to rotation about a fixed axis depending upon the problem's parameters and the initial conditions. Method Tensor calculus tools, asymptotic method, and kinematic equations of motion (EOM) are used. Results At a large time, the asymptotic properties of solutions and a system of linear differential equations that describes the approximate gyrostat motion are obtained. Conclusion The motion of the carrier body, which is close to the rotation around an axis, whose direction is fixed, depends upon the problem’s parameters and the initial conditions.